Question

Describe the roots of the equation shown below.

64x^2 - 16x + 1=0

A. There are two complex roots
B. There is one real, double root
C. There are two real, irrational roots
D. There are two real, rational roots​

Answer 1

B. There is one real, double root

Explanation:

For ax² + bx + c = 0, the discriminant is b² − 4ac.

If the discriminant is positive and a perfect square, there are two real, rational roots.

If the discriminant is positive and not a perfect square, there are two real, irrational roots.

If the discriminant is 0, there is one real, double root.

If the discriminant is negative, there are two complex roots.

Here, a = 64, b = -16, and c = 1.

b² − 4ac

= (-16)² − 4(64)(1)

= 0

The discriminant is 0. Therefore, there is one real, double root